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For the curve x = t^{2}  1, y = t^{2 } t tangent is parallel to xaxis where
The area, in square unit, bounded by the curves y = x^{3}, y = x^{2} and the ordinates x = 1, x = 2 is
If z and ω are two nonzero complex numbers such that z ω  = 1, and arg(z)  arg(ω)= π/2,then z̅ω is equal to
Suppose ω is an imaginary cube root of unity. If (1+ω^{2})^{m} = (1+ω^{4})^{m}, then the least positive integral value of m is
The given equation reduces to (−ω)^{m} = (−ω^{2})^{m}
⇒ ω^{m} = 1
⇒ m = 3
The differential equation which represents the family of plane curves y=exp. (cx) is
y = e^{cx}
dy/dx = c. e^{cx}
y' = cy
The differential equation representing the family of curves y^{2} = 2c(x + √c), where c>0, is a parameter, is of order and degree as follows
If y = y(x) and [(2 + sin x)∕(y + 1)(dy∕dx)] = cos x, y(0) = 1, then y (π∕2) equals
If f(x) = cos (logx), then f(x) f(y) 1/2[f(x/y) + f(xy)] has the value
If sin (sin⁻^{1} 1/5 + cos^{1} x) = 1, then x is equal to
Which is logically equivalent to "If today is Sunday, Matt cannot play hockey."?
Statements are logically equivalent to their contrapositives.
If the value of a determinants is 11, then the square of the determinant formed by its cofactor will be
How many words can be formed from the letters of the word MATHEMATICS?
\'A\' draws two cards with replacement from a pack of 52 cards and \'B\' throws a pair of dice. What is the chance that \'A\' gets both cards of same suit and \'B\' gets total of 6?
The probabiltiy that the two digit number formed by digits 1,2,3,4 is divisible by 4, is
A single letter is selected at random from the word PROBABILITY. The probability that it is a vowel is
The fourth ,seventh and tenth of a G.P. are p,q,r respectively then
Which of the following measures of marks is the most suitable one of central location for computing intelligence of students?
A batsman scores runs in 10 innings 38, 70, 48, 34, 42, 55, 63, 46, 54 and 44, then the mean deviation is
In equation 2^{x+1}2^{x}=2^{x}1+1 the values of x are
The equation of the sphere concentric with the sphere x^{2}+y^{2}+z^{2}4x6y8z=0 and which passes thro' (0.1,0) is
If √2 + √3 + i be one of the roots of a given equation f(x) = 0 with real coefficients, then the lowest degree of such an equation must be____
Since the complex and irrational roots occure in pairs, therefore, if one root is 2 + √3 + i , then the other roots are
The equation of the sphere concentric with the sphere x^{2}+y^{2}+z^{2}  4x  6y  8z  5 = 0 and which passes through the point (0, 1, 0) is
If m_{1}, m_{2} are slopes of the two tangents that are drawn from (2, 3) to the parabola y^{2} = 4x, then the value of [(1/m_{1}) + (1/m_{2})] is
If P is any point on the hyperbola [(x  1)^{2}/9  (y + 1)^{2}/16] = 1 and S_{1}, S_{2} are its foci, then  s_{1} P  S_{2} P 
The values of 'θ' satisfying sin 7θ = sin 4θ  sin θ in 0 < θ < π/2 are
sin 7θ + sin θ  sin 4θ = 0
⇒ 2 sin 4θ . cos 3θ  sin 4θ = 0
⇒ sin 4θ [2 cos 3θ  1] = 0
⇒ sin 4θ = 0 or cos 3θ = 1/2 = cos ( π/3 )
⇒ 4θ = nπ or 3θ = 2nπ ( π/3 )
⇒ θ = nπ/4 or θ = ( 2nπ/3 ) ( π/9 )
∴ The values of θ are π/4 , π/9
The volume of parallelopiped whose edges are 12i+λk, 3ik, 2i+j15k respectively is 546, then λ=
The value of deBroglie wavelength of an electron moving with a speed of 6.6 x 10^{5} m s^{1} is approximately [ h = 6.6 x 10^{34} J − sec , mass of electron = 9 x 10^{31} Kg ]
A photon of energy 2.5eV and wavelength λ falls on a metal surface and the ejected electrons have a velocity 'V' . If the wave length λ of incident light is decreased by 20%, the velocity of emitted electrons is doubled, then the work function of the metal is
If sky wave with a frequency of 50 MHz is incident on Dregion at an angle of 30^{o}, then angle of refraction is
Minimum resistance of a circuit, with n resistance 'R' each combination is
A wire of length L is drawn such that its diameter is reduced to half of its original diameter. If the initial resistance of the wire were 10Ω, its new resistance would be
We have kept the volume of the wire constant i.e.
The expression for magnetic induction inside a solenoid of length L, carrying a current I and having N number of turns is
The inductance of a coil is L = 10 H and resistance R = 5 Ω . If applied voltage of battery is 10 V and it switches off in 1 millisecond, find induced emf of inductor.
The distance travelled by light in glass (refractive index =1.5) in a nanosecond will be
Speed of light in glass
Distance travelled in one nanosecond
= 2 x 10^{8} x 10^{9} = 0.2 m = 20 cm
The product acetal is produced by reacting alcohol in the presence of dry HCl with
The ratio of the molar amounts of H₂S needed to precipitate the metal ions from 20 mL each of 1M Cd(NO₃)₂ and 0.5 M CuSO₄ is
As Cd^{2+} and Cu^{2+}, both are dipositive ions but Cu^{2+} has one half of the concentration compared to that of the Cd^{2+}. Thus, the molar amount of the H_{2}S used to precipitate the metals ions Cd^{2+} and Cu^{2+} is 2 : 1.
How many monochlorobutanes will be obtained on chlorination of nbutane?
The substances which act as emulsifiers in lipid metabolism are
The following reaction is called
2 CH₃COOC₂H₅ → CH₃COCH₂COOC₂H₅
Vinegar made from cane sugar, nowadays synthetically contains
Calculate Δ H in KJ for the following reaction C(s)+ O_{2} g → CO_{2} g Given that
H_{2}O g + C g → CO g + H_{2} g , Δ H = + 131 k J
CO g + 1/2 O_{2} g → CO_{2} g , Δ H = − 282 k J
H_{2} g + 1/2 O_{2} g →H_{2}O g , Δ H = − 242 k J
The rate, at which a substance reacts at constant temperature, depends upon its
Which of the following ingredients is not used in sun burn creams?
Which of the following will show geometrical isomerism ?
Standard enthalpy and standard entropy changes for the oxidation of ammonia at 298 K are  382.64 kJ mol^{1} and  145.6 JK^{1} mol^{1} respectively. The standard Gibbs energy change for the same reaction 298 K is
How many EDTA (ethylenediaminetetraacetic acid) molecules are required to make an octahedral complex with a Ca^{2+} ion?
A complex compound of Co^{2+} with molecular formula CoCl_{xy}NH₃ gives a total of three ions per molecule when dissolved in water. How many Cl⁻ ions satisfy primary as well secondary valencies in this complex?
The amount of electricity that can deposit 108 g of silver from silver nitrate solution is
The quantity of electricity required to liberate 112 cm^{3} of hydrogen at STP from acidified water is
Use of hot air balloons in sports and metereological observations is an application of
When ether is exposed in air for sometime, an explosive substance produced is
Nitrogen shows different oxidation states in the range
Cuprous ion is colourless while cupric ion is coloured because
Fill in the blank with appropriate word.
Many of the advances of civilisation have been conceived by young people just on the........of adulthood
Out of the given alternatives, choose the one which can be substituted for the given capitalised word.
The police fired AT RANDOM at the violent crowd and several persons lost their lives.
Improve the sentence by choosing best alternative for capitalised part of the sentence.
Last evening I went to the optician and bought SPECTACLES
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